Displaying similar documents to “Polarized category theory, modules, and game semantics.”

μ -bicomplete categories and parity games

Luigi Santocanale (2002)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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For an arbitrary category, we consider the least class of functors containing the projections and closed under finite products, finite coproducts, parameterized initial algebras and parameterized final coalgebras, i.e. the class of functors that are definable by μ -terms. We call the category μ -bicomplete if every μ -term defines a functor. We provide concrete examples of such categories and explicitly characterize this class of functors for the category of sets and functions. This goal...

Logical consequence and the theory of games

Paul Harrenstein (2004)

Philosophia Scientiae

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Logical notions of consequence have frequently been related to game-theoretical solution concepts. The correspondence between a formula being classically valid and the existence of a winning strategy for a player in a related two-person game, has been most prominent in this context. We propose a conservative extension of the classical notion of consequence that is based on a generalization of the game-theoretical solution concept of Nash equilibrium.

On knowledge games.

J. M. Lasry, J. M. Morel, S. Solimini (1989)

Revista Matemática de la Universidad Complutense de Madrid

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We give a formalization of the ?knowledge games? which allows to study their decidability and convergence as a problem of mathematics. Our approach is based on a metalemma analogous to those of Von Neumann and Morgenstern at the beginning of Game Theory. We are led to definitions which characterize the knowledge games as objects is standard set theory. We then study rigorously the most classical knowledge games and, although we also prove that the ?common knowledge? in these games may...

Three notes on the complexity of model checking fixpoint logic with chop

Martin Lange (2007)

RAIRO - Theoretical Informatics and Applications

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This paper analyses the complexity of model checking fixpoint logic with Chop – an extension of the modal -calculus with a sequential composition operator. It uses two known game-based characterisations to derive the following results: the combined model checking complexity as well as the data complexity of FLC are EXPTIME-complete. This is already the case for its alternation-free fragment. The expression complexity of FLC is trivially P-hard and limited from above by the complexity...